Aromatic molecules with pi electrons are commonly involved in chemical and biological recognitions. For example, nucleobases play central roles in DNA/RNA structure and their interactions with proteins. The delocalization of the pi electrons is responsible for the high polarizability of aromatic molecules. In this work, the AMOEBA force field has been developed and applied to 5 regular nucleobases and 12 aromatic molecules. The permanent electrostatic energy is expressed as atomic multipole interactions between atom pairs, and many-body polarization is accounted for by mutually induced atomic dipoles. We have systematically investigated aromatic ring stacking and aromatic-water interactions for nucleobases and aromatic molecules, as well as base-base hydrogen-bonding pair interactions, all at various distances and orientations. van der Waals parameters were determined by comparison to the quantum mechanical interaction energy of these dimers and fine-tuned using condensed phase simulation. By comparing to quantum mechanical calculations, we show that the resulting classical potential is able to accurately describe molecular polarizability, molecular vibrational frequency, and dimer interaction energy of these aromatic systems. Condensed phase properties, including hydration free energy, liquid density, and heat of vaporization, are also in good overall agreement with experimental values. The structures of benzene liquid phase and benzene-water solution were also investigated by simulation and compared with experimental and PDB structure derived statistical results.
We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter omega, can be made at almost no cost. This method is denoted by TCG-n(omega). Black-box adaptive methods to find good choices of omega are provided and discussed. Results show that TPCG-3(omega) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(omega) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(omega) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.
This work presents a systematic development of a new van der Waals potential (vdW2016) for common organic molecules based on symmetry-adapted perturbation theory (SAPT) energy decomposition. The Buf-14-7 function, as well as Cubic-mean and Waldman-Hagler mixing rules were chosen given their best performance among other popular potentials. A database containing 39 organic molecules and 108 dimers was utilized to derive a general set of vdW parameters, which were further validated on nucleobase stacking systems and testing organic dimers. The vdW2016 potential is anticipated to significantly improve the accuracy and transferability of new generations of force fields for organic molecules.
Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 A is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. (c) 2016 Wiley Periodicals, Inc.
Molecular recognition is of paramount interest in many applications. Here we investigate a series of host-guest systems previously used in the SAMPL4 blind challenge by using molecular simulations and the AMOEBA polarizable force field. The free energy results computed by Bennett's acceptance ratio (BAR) method using the AMOEBA polarizable force field ranked favorably among the entries submitted to the SAMPL4 host-guest competition [Muddana, et al., J. Comput.-Aided Mol. Des., 2014, 28, 305-317]. In this work we conduct an in-depth analysis of the AMOEBA force field host-guest binding thermodynamics by using both BAR and the orthogonal space random walk (OSRW) methods. The binding entropy-enthalpy contributions are analyzed for each host-guest system. For systems of inordinate binding entropy-enthalpy values, we further examine the hydrogen bonding patterns and configurational entropy contribution. The binding mechanism of this series of host-guest systems varies from ligand to ligand, driven by enthalpy and/or entropy changes. Convergence of BAR and OSRW binding free energy methods is discussed. Ultimately, this work illustrates the value of molecular modelling and advanced force fields for the exploration and interpretation of binding thermodynamics.
Diffusion of transmembrane and peripheral membrane-bound proteins within the crowded cellular membrane environment is essential to diverse biological processes including cellular signaling, endocytosis, and motility. Nonetheless we presently lack a detailed understanding of the influence of physiological levels of crowding on membrane protein diffusion. Utilizing quantitative in vitro measurements, here we demonstrate that the diffusivities of membrane bound proteins follow a single linearly decreasing trend with increasing membrane coverage by proteins. This trend holds for homogenous protein populations across a range of protein sizes and for heterogeneous mixtures of proteins of different sizes, such that protein diffusivity is controlled by the total coverage of the surrounding membrane. These results demonstrate that steric exclusion within the crowded membrane environment can fundamentally limit the diffusive rate of proteins, regardless of their size. In cells this "speed limit" could be modulated by changes in local membrane coverage, providing a mechanism for tuning the rate of molecular interaction and assembly.
We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short-range charge penetration correction modifying the charge-charge, charge-dipole and charge-quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry-Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono- and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER-HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration-corrected polarizable force fields highlighting the mandatory need of non-spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short-range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio- or bioinorganic systems in periodic boundary conditions.
The principal challenge of using classical physics to model biomolecular interactions is capturing the nature of short-range interactions that drive biological processes from nucleic acid base stacking to protein-ligand binding. In particular most classical force fields suffer from an error in their electrostatic models that arises from an ability to account for the overlap between charge distributions occurring when molecules get close to each other, known as charge penetration. In this work we present a simple, physically motivated model for including charge penetration in the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) force field. With a function derived from the charge distribution of a hydrogen-like atom and a limited number of parameters, our charge penetration model dramatically improves the description of electrostatics at short range. On a database of 101 biomolecular dimers, the charge penetration model brings the error in the electrostatic interaction energy relative to the ab initio SAPT electrostatic interaction energy from 13.4 kcal mol-1 to 1.3 kcal mol-1. The model is shown not only to be robust and transferable for the AMOEBA model, but also physically meaningful as it universally improves the description of the electrostatic potential around a given molecule.
BACKGROUND: Dietary canthaxanthin (CX), 25-hydroxycholecalciferol (25-OH-D 3 ) and vitamins have been widely reported to be involved in productive and reproductive performance of broiler breeders. However, limited information is available for duck breeders. In this study, a total of 1,560 Cherry Valley SM3 duck breeder females and 312 males were used to assess if the addition of CX and 25-OH-D3 could increase the performance of duck breeders under two different dietary vitamin regimens. Four diets were used under a 2 x 2 factorial arrangement with 2 kinds of vitamin premixes (REGULAR and HIGH; HIGH premix had higher levels of all vitamins except K3 than REGULAR premix), and with or without the supplementation of the mixture of CX (6 mg/kg) and 25-OH-D3 (0.069 mg/kg). The ducks were fed ad libitum with pelleted diets based on corn-soybean meal from 38 to 77 wk of age. RESULTS: HIGH vitamin premix decreased malondialdehyde (MDA) level (P < 0.001) of egg yolk, increased hatchability of fertile eggs (P = 0.029), increased hatchability of total eggs (P = 0.029), and decreased serum protein carbonyl level (P = 0.037) of breeder males. The mixture of CX and 25-OH-D3 increased serum calcium of breeder females (P = 0.010), decreased the cracked egg rate (P = 0.001), increased the pigmentation of egg yolk (P < 0.001) and male bill (P < 0.001), and decreased MDA level of egg yolk (P < 0.001) and male serum (P = 0.034). Interactive effects were observed in cracked egg rate (P = 0.038), shell thickness (P = 0.011) and serum phosphorus (P = 0.026) of breeder females. HIGH vitamin premix together with the mixture of CX and 25-OH-D3 decreased cracked egg rate and increased shell thickness of duck breeders. Serum phosphorus was decreased in duck breeder females fed REGULAR vitamin premix without the addition of the CX and 25-OH-D3 mixture. CONCLUSIONS: Dietary HIGH vitamin premix increased antioxidant status of eggs and breeder males, and increased hatchability. The mixture of CX and 25-OH-D3 enhanced egg shell quality, and promoted pigmentation and antioxidant status of eggs and breeder males.
Phosphate groups are commonly observed in biomolecules such as nucleic acids and lipids. Due to their highly charged and polarizable nature, modeling these compounds with classical force fields is challenging. Using quantum mechanical studies and liquid-phase simulations, the AMOEBA force field for dimethyl phosphate (DMP) ion and trimethyl phosphate (TMP) has been developed. On the basis of ab initio calculations, it was found that ion binding and the solution environment significantly impact both the molecular geometry and the energy differences between conformations. Atomic multipole moments are derived from MP2/cc-pVQZ calculations of methyl phosphates at several conformations with their chemical environments taken into account. Many-body polarization is handled via a Thole-style induction model using distributed atomic polarizabilities. van der Waals parameters of phosphate and oxygen atoms are determined by fitting to the quantum mechanical interaction energy curves for water with DMP or TMP. Additional stretch-torsion and angle-torsion coupling terms were introduced in order to capture asymmetry in P-O bond lengths and angles due to the generalized anomeric effect. The resulting force field for DMP and TMP is able to accurately describe both the molecular structure and conformational energy surface, including bond and angle variations with conformation, as well as interaction of both species with water and metal ions. The force field was further validated for TMP in the condensed phase by computing hydration free energy, liquid density, and heat of vaporization. The polarization behavior between liquid TMP and TMP in water is drastically different.
Classical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge-charge function previously reported (Piquemal J.-P.; J. Phys. Chem. A2003, 107, 10353) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101x7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (Parker T. M.; J. Chem. Phys.2014, 140, 094106). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields.
In this article, we present a parallel implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The smooth particle mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the direct inversion in the iterative subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy and force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package, which is the first implementation of a polarizable model that makes large-scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of SPME and a noticeable improvement of the memory management, giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to nonoptimized, sequential implementations, giving new directions for polarizable molecular dynamics with periodic boundary conditions using massively parallel implementations.
We report the development of a united AMOEBA (uAMOEBA) polarizable water model, which is computationally 3-5 times more efficient than the three-site AMOEBA03 model in molecular dynamics simulations while providing comparable accuracy for gas-phase and liquid properties. In this coarse-grained polarizable water model, both electrostatic (permanent and induced) and van der Waals representations have been reduced to a single site located at the oxygen atom. The permanent charge distribution is described via the molecular dipole and quadrupole moments and the many-body polarization via an isotropic molecular polarizability, all located at the oxygen center. Similarly, a single van der Waals interaction site is used for each water molecule. Hydrogen atoms are retained only for the purpose of defining local frames for the molecular multipole moments and intramolecular vibrational modes. The parameters have been derived based on a combination of ab initio quantum mechanical and experimental data set containing gas-phase cluster structures and energies, and liquid thermodynamic properties. For validation, additional properties including dimer interaction energy, liquid structures, self-diffusion coefficient, and shear viscosity have been evaluated. The results demonstrate good transferability from the gas to the liquid phase over a wide range of temperatures, and from nonpolar to polar environments, due to the presence of molecular polarizability. The water coordination, hydrogen-bonding structure, and dynamic properties given by uAMOEBA are similar to those derived from the all-atom AMOEBA03 model and experiments. Thus, the current model is an accurate and efficient alternative for modeling water.